The f (R, Σ, T ) Framework and Matter-Geometry Interaction: A New Perspective on Gravity

The purpose of this study is to investigate the cosmological implications of the recently proposed gravity framework known as f (R, Σ, T ). This framework extends modified gravity theories by incorporating the Ricci scalar R, a non-metricity-like scalar Σ, and the trace of the energy-momentum tensor T into the gravitational action. We take into consideration the particular functional form f (R, Σ, T ) = R + Σ + 2πηT , where η is a free coupling parameter that determines the degree to which matter and geometry interact with one another. We derive the modified field equations and establish analytic expressions for cosmic energy density and pressure in terms of the Hubble parameter and its derivative. This is done under the assumption that the Friedmann-Robertson-Walker (FRW) universe is isotropic, homogeneous, and spatially flat. A comparison is made between the cosmological model that was developed and the observational data obtained from the Pantheon+SH0ES Type Ia Supernovae sample as well as the 33 Hubble parameter measurements obtained from the Cosmic Chronometer technology. To constrain the model parameters H 0 , η, and b, we use a Bayesian statistical framework and run a Markov Chain Monte Carlo (MCMC) analysis with the emcee Python program. Our findings support an accelerating universe and suggest that the f (R, Σ, T ) model could be a viable alternative to classic dark energy theories. This is accomplished by providing more complex gravitational dynamics through longer matter-geometry couplings.